| Instructor: Gábor Hetyei | Last update: Monday, April 23, 2007 |
| Disclaimer: The information below comes with no warranty. If, due to typographical error, there is a discrepancy between the exercises announced in class and the ones below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise shows up below, I will allow you extra time to hand in the exercise that was announced in class. If, however, exercises are missing because this page is not up to date, it is your responsibility to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date. |
The deadlines do not apply to the Bonus questions,
which expire only once we solve them in class, or on April 28 at
latest.
Notation: 5.1/8a means exercise 8, part a, in chapter 5,
section 1.
| No. | Date due: | Problems: |
| 13 | Mo Apr 30 | 9.1/4 (see 9.1/Example 2 for explanation of the notation); 9.3/2ab, 4cd, 10a. |
| 12 | Mo Apr 23 |
11.2/2bd,4bd,6,8a Bonus: Describe how the winning strategy of playing NIM needs to be modified, if the player picking up the last straw loses. (Any number of straws may be taken, but only from one heap at a time.) Illustrate the strategy by finding out who can win if we start with (1,3,5,7) straws in four heaps. (This is the game in the movie "Last year in Marienbad", by Alain Resnais. You may play it online at this site, authored by Barbara Kaskosz.) |
| 11 | Mo Apr 16 |
8.2/28 reassigned with more hints, 11.1/2,4,8c. Board problems:
|
| 10 | Mo Apr 9 | 8.2/28 for n=3 and n=4; 7.2/2,4,8abc |
| 9 | Mo Apr 23 | Assignment 9 |
| 8 | Mo Mar 19 |
8.1/2,4,8,10; 8.2/2,4,8 (for n=3 only).
Bonus: 8.2/6; prove that the number cn,r of permutations on n elements with r cycles satisfies the recursion formula |
| 7 | Mo Mar 12 |
7.1/10 (reassigned with a few more hints) 7.5/6, 12b, 16ab Board problem: please download it and solve it. |
| 6 | Mo Feb 26 |
7.1/2ab, 4, 6a, 8, 10, 18; 7.3/2,6 Bonus: 7.1/12. |
| 5 | Mo Feb 19 | 6.5/2ad, 6. |
| 4 | Mo Feb 12 Extended to Mo Feb 19 |
6.4/2,6,10. Our first test is on Monday February 12. You may download the (corrected version) of the sample test I distributed in class. |
| 3 | Mo Feb 5 |
6.1/2, 6, 8a; 6.2/2, 4, 12a; 6.3/2, 4a Bonus: 6.1/16, 22. |
| 2 | Mo Jan 29 | 5.1/8a, 24; 5.2/2, 14a; 5.3/8; 5.4/4, 6, 12a, 38; 5.5/14acd |
| 1 | Mo Jan 22 | Assignment 1 |